I'm going to take a random guess here... As I am not nearly experienced as many of the people on this forum, I am sure that someone will poke a hole in this theory semi-quickly (which is a good thing), but it can't hurt to try.
Considering, just from the video, you do not have the laptop plugged in, there could be a bad wire from the battery, or power supply all together. When you press in the right spot, the wire moves a little and either makes bad contact or just makes no contact at all. The reason why I thought that it might not just be something wrong with the display is since the laptop shut completely off when the display turned off, rather than just making the screen go black. The screen flickering, (this one is most likely way off target) could be caused by the bad connection, so the screen doesn't get the power it needs. Seen similarly to when a light bulb dims because of lack of power.
